Introduction to Statistics

CHAPTER

1 Introduction to Statistics

In introducing this book to you, we assume you are a college student who is taking what is perhaps your first course in statistics to fulfill a requirement for your major or a general Chapter Outline education requirement. If so, you may be asking yourself two 1.1 What Is Statistics? questions: 1.2 Why Learn Statistics? • What is statistics? 1.3 Introduction to the Stages of the Research Process • Why learn statistics? distribute • Developing a research The ultimate goal of this book is to help you begin to answer hypothesis to be tested these two questions. {{Identifying a question or or issue to be examined {{ Reviewing and evaluating 1.1 What Is Statistics? relevant theories and research {{Stating a research Whether or not you are aware of it, you encounter a variety hypothesis: Independent of “statistics” in your day-to-day activities: the typical cost of and dependent variables going to college, the yearly income of the average college grad- • Collecting data uate, the average price of a home, and sopost, on. So what exactly {{Drawing a sample from a is “statistics”? The Merriam-Webster dictionary defines statis- population tics as a branch of mathematics dealing with the collection, {{Determining how variables analysis, interpretation, and presentation of masses of numer- will be measured: Levels of ical data. When people think about statistics, they often focus measurement on only the “analysis” aspect of the above definition—that is {{Selecting a method to collect to say, they focus on numbers that result from analyzing data. the data: Experimental and However, statisticscopy, is not only concerned about how data are non-experimental research analyzed, it recognizes the importance of understanding how methods data are collected and how the results of analyses are inter- • Analyzing the data preted and communicated. The purpose of this book is to {{Calculating descriptive introduce, describe, and illustrate the role of statistics within statistics the larger research process. not {{ Calculating inferential statistics • Drawing a conclusion regarding 1.2 Why Learn Statistics? the research hypothesis • Communicating the findings DoWe believe there are a variety of reasons why you should of the study learn statistics. First, not only do you currently encounter

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. statistics in your daily activities, but throughout your life, you Chapter Outline (continued) have been and will continue to be affected by the results of research and statistical analyses. Which college or graduate 1.4 Plan of the Book school you attend is based in part on test scores developed by 1.5 Looking Ahead psychologists. You may also have to take a personality or intel- 1.6 Summary ligence test to get a job. The choices of drugs and medicines 1.7 Important Terms available to you are based on medical research and statistical analyses. If you have children, their education may be affected 1.8 Exercises by their scores on achievement or aptitude tests. Learning about statistics will help you become a more informed and aware consumer of research and statistical analyses that affect many aspects of your life. A second reason for learning statistics is that you may be asked or required to read and interpret the results of statistical analyses. Many college courses require students to read academic research journal articles. Evaluating published research is complicated by the fact that different people studying the same topic may come up with diverse or even opposing conclusions. Understanding statistics and their role in the research process will help you decide whether conclusionsdistribute drawn in research articles are appropriate and justified. Another reason for learning statistics is that it will be of use to you in your own research. College courses sometimes have students design and conduct mini-researchor studies; undergraduate majors might require or encourage students to do senior honors theses; graduate research programs often require masters’ theses and doctoral dissertations. Learning to collect and analyze data will help you address your own questions in an objective, systematic manner. A final reason for learning statistics is that it may help you in your future career. The web- site Careercast.com conducts an annual survey in which they evaluate 200 professions on five dimensions: environment, income, employment outlook, physical demands, and stress. In 2013, the highest rated profession in this survey was “actuary,”post, defined as someone who “interprets statistics to determine probabilities of accidents, sickness, and death, and loss of property from theft and natural disasters.” Talking about his job, one actuary noted, “I can count on one hand the number of days I’ve said, ‘I don’t want to go to work today’ . . . I’ve seen people come in to say thank you for the work I’ve done. That’s pretty powerful.” It is generally a good idea for students to maintain a healthy level of curiosity or even skepticism in regards to their education. However, we find that when it comes to learning statistics, the frame of mind of some students may be characterized as one of fear and anxiety. Although we understand these feelings, we hope the benefitscopy, associated with learning statistics will become clear to you and help you overcome any concerns you may have.

1.3 Introductionnot to the Stages of the Research Process

Much of scientific research involves asking questions. Throughout this book, we will examine howDo contemporary researchers have asked and attempted to answer a broad range of questions

2 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. regarding human attitudes and behavior. Below are research questions we will address in this chapter to introduce the stages of the research process:

• Is students’ performance on tests more influenced by their learning strategies (how they learn) or their motivation (why they learn)? • Do college students and faculty differ in their beliefs about the prevalence of student academic misconduct such as cheating and plagiarism? • Is the extent to which adolescents are exposed to violence in their community related to how they do in school? • Is one method of disciplining one’s children more effective than another? • Does playing online computer games affect one’s interpersonal relationships? • Does providing substance abuse treatment to drug users have an effect on safety in the workplace?

How might you try to answer questions such as these? You could base your answers on your personal beliefs, or you could adopt the answers given to you by others.distribute But rather than relying on subjective beliefs and feelings, researchers test their ideas using science and the scientific method. The scientific method is a method of investigation that uses the objective and systematic collection and analysis of empirical data to test theoriesor and hypotheses. At its simplest, this book will portray the scientific method as consisting of five main steps or phases:

• developing a research hypothesis to be tested, • collecting data, • analyzing the data, • drawing a conclusion regarding thepost, research hypothesis, and • communicating the findings of the study.

Accomplishing each of these five steps requires completing a number of tasks, as shown in Figure 1.1. Because this sequence of steps will be used throughout this book and will serve as the model for the wide assortment of research studies we will review and discuss, each step is briefly introduced below. It is important to understand that the research process depicted in Figure 1.1 represents an ideal way of doing research. The “real” way, as you may discover in your own efforts or from speaking withcopy, researchers, is often anything but a smooth ride but rather is filled with starts and stops, dead ends, and wrong turns.

Developing a Research Hypothesis to Be Tested The notinitial stage—and the first step—of the research process is to develop a research hypothesis to be tested. A research hypothesis is a statement regarding an expected or predicted relationship between variables. A variable is a property or characteristic of an object, event, or person that can take on different values. One example of a variable is “U.S. state,” a variable with 50 possible values Do(Alabama, Arkansas, etc.).

Chapter 1 | Introduction to Statistics 3

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. Figure 1.1 Steps in the Research Process Within the Scientific Method

Develop a research hypothesis to be tested | Identify a question or issue of interest Review and evaluate relevant theory and research State a research hypothesis | Collect data | Draw a sample from a population Determine how the variables will be measured Select a method to collect the data distribute | Analyze the data | or Calculate descriptive statistics Calculate inferential statistics | Draw a conclusion regarding the research hypothesis | Communicate the findingspost, of the study

Research hypotheses are usually developed through the completion of several tasks:

• identifying a question or issue to be examined, • reviewing and evaluating relevant theories and research, and • stating a research hypothesis.copy, Each of these three tasks is described below.

Identifying a Question or Issue to Be Examined Most research startsnot with a question posed by the researcher. These questions often come from the researcher’s own ideas and daily observations. Although this may not seem terribly scientific, there is an advantage in using one’s own experience as a starting point: People are generally much more motivated to explore a question or topic that concerns them personally. In teaching statistics, we frequently advise students developing their own research projects to study something that is of interestDo to them. Conducting research can be tedious, difficult, and frustrating. At various points

4 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. during your research, you may ask yourself, “Why am I doing this?” Being able to provide a sat- isfactory answer to this question will help you overcome whatever obstacles you encounter along the way.

Reviewing and Evaluating Relevant Theories and Research Beyond the researcher’s own curiosity, research questions often arise from an examination of the theories, ideas, and research of others. A theory is a set of propositions used to describe or explain a phenomenon. The purpose of a theory is to summarize and explain specific facts using a logically consistent framework. Placing a question within a theoretical framework provides guidance and structure to research. Reviewing and evaluating existing theories and research helps the researcher decide whether it is worth the time and energy required to conduct the study. By seeing what others have done, the researcher may decide that a particular idea has already been investigated and there is no reason to duplicate earlier efforts. On the other hand, the researcher may conclude that the current way of thinking is incomplete or mistaken. By doing this review, researchers are able to ensure that the studies they undertake add to and improve upon an existing body of knowledge.distribute Stating a Research Hypothesis: Independent and Dependent Variables Understanding and evaluating an existing literature not only helps articulate a question of interest but also may lead to a predicted answer to that question. Withinor the scientific method, this answer is stated as a research hypothesis, defined earlier as a statement regarding an expected or predicted relationship between variables. Table 1.1 lists the research questions and research hypotheses for the studies listed at the beginning of this section. For example, the first research hypothesis states that “students who are taught effective learning skills will perform better on tests than students offered incentives to do well.” One characteristic of research hypotheses such as those listed in Table 1.1 is that they identify the variables that are the focus of their researchpost, studies. As mentioned earlier, a variable is a property or characteristic with different values. Variables can be classified in several ways. In specifying a research hypothesis, researchers often speak in terms of “independent” and “dependent” variables. An independent variable may be defined as a variable manipulated by the researcher. A dependent variable, on the other hand, is a variable measured by the researcher. Researchers are interested in examining the effect of the independent variable on the dependent variable. Consider the first research hypothesis provided in Table 1.1: “Students who are taught effective learning skills will perform better on tests than students who are offered incentives to do well.” Here the independentcopy, variable is the instructional method by which students are taught, which consists of two values: learning skills and incentives. The dependent variable is the test performance that will be measured during the research. In this study, the effect of the independent variable on the dependent variable is that differences in students’ test performance (the dependent variable)not may “depend” upon which instructional method (learning skills or incentives) a student receives. Table 1.2 lists the independent and dependent variables for each of the research hypotheses in Table 1.1. A second characteristic of research hypotheses, in addition to identifying variables, is that they specify with as much precision as possible the nature and direction of the relationship Dobetween variables. For example, the first research hypothesis in Table 1.1 states that “students

Chapter 1 | Introduction to Statistics 5

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. Table 1.1 Examples of Research Questions and Hypotheses

Research Question Research Hypothesis

Is students’ performance on tests more influenced Students who are taught effective learning skills by their motivation (why they learn) or their learning will perform better on tests than students offered strategies (how they learn)? incentives to do well.

Do college students and faculty differ in their Faculty members’ beliefs about the frequency of beliefs about the prevalence of student academic student academic misconduct will be lower than misconduct (i.e., cheating, plagiarism)? students’ beliefs.

Is there a relationship between adolescents’ The more adolescents are exposed to violence in exposure to violence in their community and their their community, the lower their levels of academic academic achievement? achievement.

Is one method of disciplining children more effective Children will rate a disciplining strategy that than another? emphasizes logic and reason as more effective than one based on rewards and punishment.distribute Does playing online games affect one’s interpersonal Heavy users of online games have less fulfilling relationships? interpersonal relationships than users spending little or no time playing onlineor games. Does providing substance abuse treatment to drug Drug users are less likely to have work-related users have an effect on safety in the workplace? accidents after undergoing substance abuse treatment than before the treatment. post, Table 1.2 Research Hypotheses and Their Independent and Dependent Variables

Research Hypothesis Independent Variable Dependent Variable

Students who are taught effective learning skills Instructional method Test performance will perform better on tests than students offered incentives to do well. copy, Faculty members’ beliefs about the frequency of Member of college Beliefs about the student academic misconduct will be lower than community frequency of student students’ beliefs. academic misconduct

The more adolescents are exposed to violence in Exposure to Academic achievement their community,not the lower their levels of academic community violence achievement.

Children will rate a disciplining strategy that Parental discipline Effectiveness of parental emphasizes logic and reason as more effective than strategy discipline strategy oneDo based on rewards and punishment.

6 Fundamental Statistics for the Social and Behavioral Sciences

Heavy users of online games have less fulfilling Online game-playing Quality of interpersonal interpersonal relationships than users spending little or relationships no time playing online games. Drug users are less likely to have work-related Time Occurrence of a work- accidents after undergoing substance abuse treatment related accident than before the treatment.

who are taught effective learning skills will perform better on tests. . . .” The word better indicates the nature and direction of the relationship between the independent variable (instructional method) and the dependent variable (test performance). The direction of the relationship would not have been stated if the hypothesis had included the less specific phrase “will perform differently on tests,” which simply indicates that the two groups are not expected to be the same. Table 1.3 provides directional and non-directional research hypotheses for the research studies from Table 1.1. The ability to form a directional research hypothesis is dependentdistribute on the state of the existing literature on the question of interest. If little or perhaps conflicting research has been conducted, researchers may not be able to form a directional hypothesis before they begin their research. One study, for example, examined the relationship between exerciseor deprivation (not allowing people to get their exercise) and tension, depression, and anger (Mondin et al., 1996). The researchers for the

Table 1.3 Directional and Non-directional Research Hypotheses Directional Research Hypothesis post,Non-directional Research Hypothesis Students who are taught effective learning Students who are taught effective learning skills will skills will perform better on tests than students perform differently on tests than students offered offered incentives to do well. incentives to do well. Faculty members’ beliefs about the frequency Faculty members’ beliefs about the frequency of student of student academic misconduct will be lower academic misconduct will be different than students’ than students’ beliefs. beliefs. The more adolescents are exposed to violence The more adolescents are exposed to violence in their in their community,copy, the lower their levels of community, the more different their levels of academic academic achievement. achievement. Children will rate a disciplining strategy that Children will rate a disciplining strategy that emphasizes emphasizes logic and reason as more effective logic and reason differently than one based on rewards than one based on rewards and punishment. and punishment. Heavynot users of online games have less fulfilling The quality of interpersonal relationships is different for interpersonal relationships than users spending heavy users of online games than users spending little or little or no time playing online games. no time playing online games. Drug users are less likely to have work-related The likelihood of drug users having work-related accidents after undergoing substance abuse accidents is different after undergoing substance abuse Dotreatment than before the treatment. treatment than before the treatment.

Chapter 1 | Introduction to Statistics 7

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. study reported, “We did not have a directional hypothesis, and when participants asked what we expected to find in this study, we replied: ‘We really are not sure since the results of earlier work on exercise deprivation are mixed’” (p. 1200). Collecting Data Once a research hypothesis has been formulated, researchers are ready to proceed to the second stage in the research process: collecting data relevant to this hypothesis. This step is seen as being composed of three tasks:

• drawing a sample from a population, • determining how the variables will be measured, and • selecting a method by which to collect the data.

Learning Check 1: distribute Reviewing What You’ve Learned So Far or 1. Review questions b. “It was expected that . . . greater amounts of television a. What are the main steps involved in viewing . . . would predict the research process? greater . . . posttraumatic stress b. Why is it useful to review and symptoms” (McLeish & Del Ben, evaluate theories and research before 2008). conducting a study? post,c. “We . . . hypothesized persons who c. What are the two main characteristics estimated the HSAS level to be red of research hypotheses? (severe) or orange (high) . . . when d. What is the difference between the HSAS level was [in fact] yellow an independent variable and a (elevated), would report greater dependent variable? worry about terrorism” (Eisenman 2. Listed below are several research et al., 2009). hypotheses from publishedcopy, studies. For d. “We hypothesized that each research hypothesis, identify the prekindergarten children who independent and dependent variable. participated in the 6-week intervention would perform better a. “College students will rate instructors [on a test of literacy skills] than who dress formally (i.e., business not their peers in a control group who suit and tie) as having more expertise did not participate in the program” than instructors who dress casually (Edmonds, O’Donoghue, Spano, & (i.e., slacks and shirt)” (Sebastian & Algozzine, 2009, p. 214). Do Bristow, 2008).

8 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. Drawing a Sample From a Population The first step in collecting data is to identify the group of participants to which the research hypothesis applies. The group to which the results of a study may be applied or generalized is called a population. A population is the total number of possible units or elements that could potentially be included in a study. For example, researchers could variously define the population of interest for the first research hypothesis in Table 1.1 as “college students,” “college students in the United States,” “college students in Georgia,” or “college students at the University of Georgia.” Researchers typically try to define their populations as broadly as possibly (e.g., “college students in the United States” rather than “college students in Georgia”) to maximize the applications or implications of their research. It is typically difficult to collect data from all members of a population. Imagine, for example, the time and money that would be needed to collect information from every college student in the United States. For this reason, researchers typically draw conclusions about populations based on information collected from a sample drawn from the population. A sample is a subset or portion of a population. Table 1.4 describes the samples used in the six studies introduced in Table 1.1. As you can see from Table 1.4, samples greatly vary in terms of their targeted population and size (the number of participants). distribute Determining How Variables Will Be Measured: Levels of Measurement The research hypotheses described in Table 1.1 involve variablesor such as instructional method, test performance, online game playing, and quality of interpersonal relationships. To conduct a research study, the researcher must determine an appropriate way to measure the variables stated in the research hypothesis. Measurement is the assignment of categories or numbers to objects or events according to rules. For example, to measure the variable “height,” a researcher might use “number of inches from the ground in bare feet” as a form of measurement. To measure a variable such as “success in college,” a student’s grade point average (GPA)post, may be obtained from school transcripts. “Self-esteem” might be measured by having people complete a questionnaire and, on the basis of their responses, be categorized as having either “low” or “high” self-esteem. As these examples demonstrate, the result of measurement is an assignment of a number or a category to each participant in the research study. Different types of variables require different forms of measurement. In recognition of these differences, researchers have identified four distinct levels for measuring variables: nominal, ordinal, interval, and ratio. The values of variables measured at the nominal level of measurement differ in category or type. The word nominal copy,implies having to do with “names,” such that we use first names and surnames as ways of distinguishing between people. Gender is an example of a nominal variable, in that it consists of categories or types (male and female) rather than numeric values. In the first research hypothesis in Table 1.1, the independent variable, instructional method, is measured at the nominal level, consisting of two categories: learning skills and incentives. Variablesnot measured at the ordinal level of measurement have values that can be placed in an order relative to the other values. Rankings (such as finishing first, second, or third in a race) and size (small, medium, large, or extra large) are familiar examples of an ordinal scale. Ordinal scales allow researchers to demonstrate that one value represents more or less of a variable than Dodo other values; however, it is not possible to specify the precise size or amount of the difference between values. For example, although you can say that a runner who finishes “first” in a race is

Chapter 1 | Introduction to Statistics 9

Research Hypothesis Study Sample Students who are taught effective learning skills “The participants were 109 juniors and seniors will perform better on tests than students offered in college . . . enrolled in three sections of an incentives to do well. educational psychology course” (Tuckman, 1996, p. 200). Faculty members’ beliefs about the frequency of “At a medium-sized public university in the student academic misconduct will be lower than northeastern U.S . . . 166 undergraduate students’ beliefs. students . . . 157 members of the faculty” (Hard, Conway, & Moran, 2006, p. 1063). The more adolescents are exposed to violence in “118 adolescents (59 girls, 59 boys) enrolled their community, the lower their levels of academic in a longitudinal study of the effects of violence achievement. exposure” (Borofsky, Kellerman, Baucom, Oliver, & Margolin, 2013, p. 383). Children will rate a disciplining strategy that “663 students enrolled in publicdistribute educational emphasizes logic and reason as more effective than institutions in Manhattan, Kansas” (Barnett, one based on rewards and punishment. Quackenbush, & Sinisi, 1996, p. 414). Heavy users of online games have less fulfilling “180 students attendingor a college in northern interpersonal relationships than users spending little Taiwan” (Lo, Wang, & Fang, 2005, p. 17). or no time playing online games. Drug users are less likely to have work-related “334 drug-test positive workers who completed accidents after undergoing substance abuse substance abuse treatment” (Elliot & Shelley, 2006, treatment than before the treatment. post,p. 132). faster than the runner who finishes “second,” you cannot specify the exact difference between the two runners’ times. The values of variables measured at the interval level of measurement are equally spaced along a numeric continuum. One example of an interval variable is the Fahrenheit scale of temperature. Here, a difference of five degrees has the same meaning anywhere along the scale; for example, the difference between 45°F and 50°F is the same as the difference between 65°F and 70°F. Many variables studied in the behavioralcopy, sciences (e.g., personality characteristics or attitudes) are considered to be measured at the interval level of measurement. Interval variables not only provide more precise and specific information than do ordinal variables, but they also fulfill the requirements of the most commonly used statistical procedures. Variables at the ratio level of measurement are identical to interval variables, with one excep- tion: Ratio scalesnot possess what is known as a true zero point, for which the value of zero (0) represents the complete absence of the variable. Variables that describe a physical dimension (such as height, weight, distance, and time duration) typically have a true zero point. In the first research hypothesis in Table 1.1, the researchers in this study measured the variable “test performance” by recording the numberDo of correct answers to a test of reading comprehension. Test performance is a ratio variable because it has a true zero point, where zero would indicate the complete absence of correct answers.

10 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. One advantage of ratio measurement versus interval measurement is that ratio variables allow for a greater number of comparisons among values. Consider, for example, the value 6 for the ratio variable “inches.” Not only is the difference between 4 and 6 inches the same as the difference between 6 and 8 inches (thereby involving addition and subtraction), 6 inches is also twice as long as 3 inches and half as long as 12 inches (involving multiplication and division). Multiplication and division comparisons cannot be made with interval variables. You cannot, for example, say that a temperature of 90°F is three times as much temperature as 30°F. The bold-faced and italicized text in Table 1.5 illustrates how the authors of the six studies described in the earlier tables chose to measure their independent and dependent variables. As you can see, the variables in these studies have been measured in a variety of ways at different levels of measurement.

Table 1.5 Research Hypotheses and Measurement of Variables

Research Hypothesis Independent Variable distributeDependent Variable Students who are taught effective learning Instructional method Test performance skills will perform better on tests than learning strategy, number of items correct students offered incentives to do well. incentive motivationor (ratio) (nominal)

Faculty members’ beliefs about the Member of college Beliefs about the frequency of frequency of student academic misconduct community student academic misconduct will be lower than students’ beliefs. faculty, student 1–5 scale (1 = Never, 5 = Very often) (nominal) (ordinal)

The more adolescents are exposed to Exposure to Academic achievement violence in their community, the lower theirpost, community violence Grade point average (GPA) levels of academic achievement. 0 times, 1 time, 2 (ratio) times, 3+ times (ratio)

Children will rate a disciplining strategy Parental discipline Effectiveness of parental discipline that emphasizes logic and reason as more strategy strategy effective than one based on rewards and power assertion, love 1–5 scale (1 = Not at all effective, punishment. copy, withdrawal, induction 5 = Very effective) (nominal) (ordinal)

Heavy users of online games have less Online game-playing Quality of interpersonal fulfilling interpersonal relationships than heavy, light, nonplayer relationships users spending little or no time playing (nominal) 1–6 scale (1 = Strongly agree, onlinenot games. 6 = Strongly disagree) (ordinal)

Drug users are less likely to have work- Time Occurrence of a work-related related accidents after undergoing before treatment, after accident Dosubstance abuse treatment than before the treatment Yes, No treatment. (nominal) (nominal)

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Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. What difference does the level of measurement make? A variable’s level of measurement has important implications for researchers in that it influences how research hypotheses are stated as well as how data are analyzed. For example, imagine you are interested in studying the variable “success in college.” You could choose to measure this variable at the nominal level of measurement by having faculty members classify students into one of two groups: successful or unsuccessful. Researchers typically employ nominal variables when they are interested in questions involving differences between groups, such as, “Do successful and unsuccessful college students differ in their study habits?” You could instead measure success in college as an ordinal variable by having faculty members rank their students from top to bottom. Ranking enables a researcher to study relative differences with less concern for the precise magnitude of these differences. For example, using ranked data, you could ask, “How similar are younger and older faculty members’ rankings of their students?” To study success in college using the interval level measurement, you could have faculty members rate each student on a scale from 1 (low) to 100 (high). You could then use these ratings to address a research question such as, “Is there a relationship between faculty members’ ratings of their students and students’ ratings of themselves?” distribute Finally, to measure success in college using the ratio level of measurement, you could use students’ salary after graduation (in dollars) as an indicator of success. Salary is a ratio variable because it contains a true zero point. In practice, ratio variables can be usedor to ask many of the same questions as those involving interval variables. For example, you could ask, “Is there a relationship between faculty members’ ratings of students and students’ salaries after graduation?” As you can see, how researchers choose to measure their variables influences how they state their research questions and research hypotheses. The level of measurement used for a variable has another important implication: It helps determine the statistical procedures researchers use to analyze the data. Certain statistical procedures can be applied only to variables measured at the interval or ratio levels of measurement, whereas other procedurespost, are appropriate for variables measured at the nominal or ordinal level.

Selecting a Method to Collect the Data: Experimental and Non-experimental Research Methods In addition to drawing a sample from a population and determining how the variables in a study may be measured, the third step in collecting data is to determine the type of research method to use to collect the data on thesecopy, variables. Research methods may be classified into two main types: • experimental research methods, and • non-experimental research methods.

Experimentalnot Research Methods. Experimental research methods are methods designed to test causal relationships between variables—more specifically, whether changes in independent variables produce or cause changes in dependent variables. To make inferences about cause-effect relationships, researchers conducting an experiment must first eliminate all other possible causes or Doexplanations for changes in the dependent variable besides the independent variable. If it can be claimed that a variable other than the independent variable created the observed changes in the

12 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. Learning Check 2: Reviewing What You’ve Learned So Far

1. Review questions a. Type of school attended (public, private) a. What is the difference between a population and a sample? b. Probability of graduating college in 4 b. Within the research process, what is years (0% to 100%) the relationship between populations c. Rating of television (good, better, and samples? best) c. What are the four levels of d. Number of computers in home measurement? How do they differ? 2. For each of the following variables, name the scale of measurement distribute (nominal, ordinal, interval, or ratio). or dependent variable, the research results are said to be confounded. A confounding variable is a variable related to an independent variable that provides an alternative explanation for the relationship between the independent and dependent variables. To understand how confounding variables work, consider the following question: What is the relationship between a mother’s ethnicity and the birth weight of her baby? Although research has shown differences in the birth weights of babies of different ethnicities, one study noted that some of this research did not take into accountpost, the possibility that differences in birth weights may be partly due to differences between ethnic groups on such factors as the mother’s average age at time of pregnancy, socioeconomic status, and behaviors such as smoking and drinking (Ma, 2008). These lifestyle characteristics are considered confounding variables in that they provide alternative explanations for any causal relationship between ethnicity and babies’ birth weights. Researchers minimize the influence of confounding variables in two main ways. First, researchers exercise experimental control by making the research setting (i.e., characteristics of the research participants, locationcopy, of the experiment, the instruments or measures administered, the instructions given to the research participants) the same for all participants. In the birth weight study, for example, the research design might control for the effect of parental smoking on birth weight by only including nonsmokers in the study sample, excluding those who smoke. Another way researchers exert control over the research setting is to include a condition knownnot as a control group, which is a group of participants in an experiment not exposed to the independent variable the research is designed to test. For example, if you conducted an experiment designed to examine the effects of caffeine on one’s health, one group (the experimental group) might be instructed to drink coffee while a second group (the control group) drinks decaffeinated Docoffee. By contrasting the results of the two groups, researchers can then assess the impact of caf- feinated coffee on the health of those who drink it.

Chapter 1 | Introduction to Statistics 13

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. Researchers cannot possibly identify and control for the effects of all potential confounding variables. Consequently, a second strategy used to minimize the influence of confounding variables is random assignment, which is assigning participants to each category of an independent variable in such a way that each participant has an equal chance of being assigned to each category. For example, to assign a participant to either the experimental or the control condition of a study, a researcher might simply flip a coin: heads for experimental, tails for control. The purpose of random assignment is to equalize or neutralize the effects of confounding variables by distributing them equally over all levels of the independent variable.

Non-experimental Research Methods. Experimental research designs are one of the best tools researchers have for making causal inferences. However, the ability to make causal inferences requires a great deal of control over the situation, control that may not always be possible or desirable. For this reason, researchers often employ non-experimental research methods (sometimes referred to as correlational research methods). non-experimental research methods are research methods designed to measure naturally occurring relationships between variables without having the ability to infer cause-effect relationships. Some of the most common types of non-experimental research designs include quasi-experiments, survey research, observational research, and archival distributeresearch. Quasi-experimental research compares naturally formed or preexisting groups rather than employing random assignment to conditions. For example, suppose a researcher wanted to study the effects of different methods of teaching reading on children’s verbal skills. Ideally, the researcher would randomly assign a sample of schoolchildren to receive the ordifferent teaching methods. However, because children are taught together in classes, it would be difficult to have children in the same classroom receive different methods. Implementing multiple methods in a single classroom would not only place an unreasonable burden on the teacher, but children would also see their classmates being treated differently, which might influence their behavior. To address these concerns, a researcher might assign entire classrooms of children to receive a particular method. Comparing the classrooms is an example of quasi-experimentalpost, research. Survey research methods obtain information directly from a group of people regarding their opinions, beliefs, or behavior. The goal of survey research, which can involve the use of question- naires and interviews, is to obtain information from a sample that can then be used to represent or estimate the views of a larger population. Because the researcher does not directly manipulate any variables, survey research is not conducted to make causal inferences but is instead used to describe a phenomenon or predict future behavior. As one example of survey research, political pollsters attempt to predict how people will vote in an election by asking a sample of voters about their preferences. Observational researchcopy, is the systematic and objective observation of naturally occurring behavior or events. The purpose of observational research is to study behavior or events, with little, if any, intervention on the part of the researcher. Observational research is often used to study phenomena that the researcher either cannot or should not deliberately manipulate. For example, researchers studying aggressive behavior in children would never force children to push or hit each other. By observingnot playground behavior, however, researchers may be able to record acts of aggression if and when they occur. Rather than observing or measuring behavior directly, archival research is the use of archives (records or documents of the activities of individuals, groups, or organizations) to examine research questionsDo or hypotheses. One example of an archival research study was interested in studying criminal trials—more specifically, whether the race, age, or gender of an offender is related to the

14 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. severity of the sentence they receive (Steffensmeier, Ulmer, & Kramer, 1998). To conduct their study, they obtained and analyzed state court records of more than 138,000 criminal trials, recording the severity of the sentences given to the offender as well as the offender’s race, age, and gender.

An Example of Combined Experimental and Non-experimental Research. Both experimental and non-experimental research methods have strengths and weaknesses. The strength of experimental research is the ability to demonstrate cause-effect relationships between independent and dependent variables; however, the control that experiments require creates situations that may not resemble the real world. Non-experimental research methods do not allow the researcher to make causal inferences because they do not involve experimental manipulation, experimental control, or random assignment; however, they have the advantage of allowing researchers to study variables as they naturally occur. Given the strengths and limitations of both research methods, one solution is to use and compare the findings from both methods for examining the same question. Does playing violent video games lead to aggressive behavior? Two researchers studied this important question using both experimental and non-experimental research methods, saying, “We chose two different methodologies that have strengths that complement each other and surmount each others’ weaknesses” (Anderson & Dill, 2000, p. 776). distribute For their experiment, participants were randomly assigned to one of two conditions, playing either a violent video game or a nonviolent game; “type of video game” was their independent variable. Next, they played another type of game in which they orcould punish their opponent (who was actually a computer) by delivering a loud blast of noise. The loudness and duration of the noise delivered by participants represented the dependent variable of “aggressive behavior.” For their non-experimental method, the researchers used a survey methodology, asking students to fill out a questionnaire about the number of hours they played violent video games each week (the independent variable). For the dependent variable of aggressive behavior, students reported the number of times in the previous year that they had performed eight different aggressive acts, such as hitting or stealing from other students.post, What did the researchers find? In reporting their findings, they wrote, “In both a correlational investigation using self-reports of real-world aggressive behaviors and an experimental investigation using a standard, objective laboratory measure of aggression, violent video game play was posi- tively related to increases in aggressive behavior” (Anderson & Dill, 2000, p. 787). In evaluating their study, they emphasized the advantages of using both types of research methods, explaining that the non-experimental method “measured video game experience, aggressive personality, and delinquent behaviorcopy, in real life . . . [whereas] an experimental methodology was also used to more clearly address the causality issue” (p. 782).

Analyzing the Data Once data have been collected, the next step in the research process involves analyzing them. This part notof the research process addresses the primary topic of this book: statistics. Because this is the first chapter of this book, we will not describe analyzing data in detail. Instead, we introduce the notion that there are two main purposes of analyzing data: (1) to organize, summarize, and describe the data that have been collected and (2) to test and draw conclusions about ideas and hypotheses. DoThese two purposes are met by calculating two main types of statistics: descriptive statistics and inferential statistics.

Chapter 1 | Introduction to Statistics 15

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. Calculating Descriptive Statistics Descriptive statistics are statistics used to summarize and describe a set of data for a variable. For example, you have probably heard of crime statistics and unemployment statistics, statistics used to describe or summarize certain aspects of our society. Using a research-related example, Caitlin Abar, a researcher at Brown University, conducted a study examining increases in students’ alcohol-related behaviors after entering college (Abar, 2012). To measure students’ level of alcohol use, she created a variable called “typical weekend drinking,” which “was measured as the sum of drinks consumed on a typical Friday and Saturday within the past 30 days” (p. 22). One way to organize and summarize students’ responses to the typical weekend drinking variable would be to calculate the mean, which is the mathematical average of a set of scores. The mean, described in Chapter 3, is an example of a descriptive statistic. The first part of this book describes a variety of descriptive statistics used by researchers to summarize data they have collected.

Calculating Inferential Statistics Besides summarizing and describing data, a second purpose of statistics is to analyze data to test hypotheses and draw conclusions. Inferential statistics are statistical procedures used to test hypotheses and draw conclusions from data collected during research studies. Bydistribute using inferential statistics, researchers are able to test the ideas, assumptions, and predictions on which their research is based. Using inferential statistics, researchers are able to make inferences about the existence of relationships between variables in populations based on information gatheredor from samples of the population. As an example of an inferential statistic, let’s return to the example of students’ alcohol-related behaviors introduced above (Abar, 2012). This study was interested in seeing whether there was a relationship between these behaviors and students’ perceptions regarding different aspects of their relationships with their parents. One of these aspects was “alcohol communications,” defined as “the extent that they discussed alcohol related topics with their parents at some point during the past several months” (p. 22). To test apost, hypothesis regarding the relationship between alcohol communications and students’ alcohol use, we may decide to use an inferential statistic known as the Pearson correlation coefficient, which will be discussed in Chapter 13. The chapters in the last half of this book discuss a broad variety of examples of inferential statistics, along with detailed instructions for analyzing and drawing conclusions from statistical data and presenting research findings.

Drawing a Conclusioncopy, Regarding the Research Hypothesis Once statistical analyses have been completed, the next step is to interpret the results of the analyses as they relate to the research hypothesis. More specifically, do the findings of the analyses support or not support the research hypothesis? The word support in the previous sentence is very important. Students andnot researchers are sometimes tempted to conclude that their findings “prove” their hypotheses are either true or false. However, as will be discussed in Chapter 5, because researchers typically do not collect data from the entire population, they cannot know with 100% certainty whether their hypothesis is in fact true or false. Also, given the complexity of the phenomena studied by researchers, it is extremely difficult for one research study to prove a hypothesis or theory is completelyDo true or false.

16 Fundamental Statistics for the Social and Behavioral Sciences

1. Review questions c. What are the main types of Non- experimental research methods? a. What are the main differences between experimental and Non- d. What are the relative strengths and experimental research methods? weaknesses of experimental and non- experimental research? b. What are confounding variables? What do researchers do to minimize e. What are the main purposes of the effects of confounding variables? descriptive and inferential statistics? distribute Communicating the Findings of the Study Conducting research requires a variety of different skills: conceptual skills to develop research hypotheses, methodological skills to collect data, and mathematicalor skills to analyze these data. Another integral part of the research process is the communication skills needed to inform others about a study. Researchers must be not only skilled scientists but also effective writers. For many years, the American Psychological Association (APA), the professional association for psychologists, has recognized the need to provide researchers guidance on how to communicate the results of their research. In 1929, the APA published a seven-page article in the journal Psychological Bulletin entitled, “Instructions in Regard to Preparation of Manuscript.” In contrast, the sixth edition of the Publication Manual of the Americanpost, Psychological Association, published in 2010, consists of 272 pages. This increase in length highlights the challenges faced by writers in communicating their research in an effective and efficient manner.

1.4 Plan of the Book

The primary purpose of this chapter was to introduce statistics and place it within the larger research process. The remaindercopy, of the book will discuss a number of different statistical procedures used by researchers to examine various questions of interest. Although it is critical for you to be able to correctly calculate statistics, it is equally important to understand the role of statistics within the research process and appreciate the conceptual and pragmatic issues related to the use (and some- timesnot misuse) of statistics. The first half of the book (Chapters 2 through 6) will introduce you to conceptual and mathematical issues that are the foundation of statistical analyses. Chapters 2, 3, and 4 discuss how data may be examined, described, summarized, and presented in numeric, visual, and graphic form. Descriptive statistics are introduced and discussed in these chapters. Chapters 5 and 6 introduce Docritical assumptions about and characteristics of the inferential statistical procedures used to test

Chapter 1 | Introduction to Statistics 17

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. research hypotheses. The remaining chapters of the book will introduce you to a number of different inferential statistical procedures, along with key issues surrounding the use of these procedures. In most cases, the chapters in this book share a uniform format and structure, and are centered on the research process. In making our presentation, we will employ various examples of actual published research studies, addressing questions with which you may be familiar. In each case, we will clearly state the research hypothesis, briefly describe how the data in the study were collected, introduce and describe the calculation of both descriptive and inferential statistics, and discuss the extent to which the results of the statistical analyses support the research hypothesis. Finally, we will illustrate how to communicate one’s research to a broader audience.

1.5 Looking Ahead

We began our presentation by defining statistics and providing reasons why learning about them may be of value to you. Next, we placed statistics within the stages of the larger research process, a process that will be the foundation of this textbook. As we have explained, the research process is centered on a research hypothesis, a predicted relationship between variables. distributeOnce a hypothesis has been stated, the next step is to collect data about the variables included in the research, after which the process of statistical analysis begins. Analyzing data involves the calculation of two main types of statistics, one designed to describe and summarize the data for a variable (descriptive statistics) and one designed to test research hypotheses (inferential statistics).or However, before conducting analyses on a set of data, there is preliminary work that must be completed. The next chapter will focus on methods used by researchers to examine data.

1.6 SUMMARY post, Statistics may be defined as a branch of math- Researchers conduct research using the ematics dealing with the collection, analysis, scientific method of inquiry, a method of inves- interpretation, and presentation of masses tigation that uses the objective and system- of numerical data. As such, statistics is not atic collection and analysis of empirical data only concerned about how data are analyzed to test theories and hypotheses. The research but also recognizes the importance of under- process used within the scientific method of standing how data are collectedcopy, and how the inquiry consists of five main steps: developing results of analyses are interpreted and com- a research hypothesis to be tested, collecting municated. data, analyzing the data, drawing a conclusion There are a variety of reasons why stu- regarding the research hypothesis, and com- dents should learn statistics: Statistics are municating the findings to the study. encounterednot in a wide variety of daily activ- A research hypothesis is a statement ities, students may be asked or required to regarding an expected or predicted relation- read and interpret the results of statistical ship between variables. Developing a research analyses in their courses, students may use hypothesis involves identifying a question or Dostatistics in conducting their own research, issue to be examined, reviewing and evaluat- and statistics may help one’s career. ing relevant theories and research, and stating

18 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. the research hypothesis to be tested in the independent variables that provide an alterna- study. A theory is a set of propositions used to tive explanation for the relationship between describe or explain a phenomenon. A research independent and dependent variables. To hypothesis contains variables, which are minimize the impact of confounding variables, properties or characteristics of some object, a research study may exercise experimental event, or person that can take on different val- control over various aspects of the situation, ues. More specifically, a research hypothesis including the use of a control group, which states the nature and direction of a proposed is a group of participants not exposed to the relationship between an independent variable independent variable the research is designed (a variable manipulated by the researcher) and to test, or random assignment, which involves a dependent variable (a variable measured by assigning participants to each category of an the researcher). independent variable in such a way that each Collecting data involves drawing a sam- participant has an equal chance of being ple from a population, determining how the assigned to each category. variables will be measured, and selecting a Examples of non-experimental research method to collect the data. A population is methods are survey research, in which infor- the total number of possible units or ele- mation is directly obtaineddistribute from a group of ments that could potentially be included in people regarding their opinions, beliefs, or a study; a sample is a subset or portion of behavior; observational research, which a population. Variables can be measured at involves theor systematic and objective observa- one of four levels of measurement: nominal tion of naturally occurring events; and archi- (values differing in category or type), ordi- val research, which uses archives (records nal (values placed in an order relative to the or documents of the activities of individuals, other values), interval (values equally spaced groups, or organizations) to examine research along a numeric continuum), or ratio (values questions or hypotheses. equally spaced along a numeric continuum Once data have been collected, the next with a true zero point). post,step is to analyze them using two main types There are two main types of methods of statistics: descriptive statistics, which used to collect data: experimental research summarize and describe a set of data, and methods, designed to test whether changes inferential statistics, which are statisti- in independent variables produce or cause cal techniques used to test hypotheses and changes in dependent variables, and Non- draw conclusions from data collected during experimental research methods, designed to research studies. examine the relationship between variables Once the statistical analyses have been without having thecopy, ability to infer cause-ef - completed, the results of the analyses are fect relationships. interpreted regarding whether they support In experimental research, researchers or not support the study’s research hypothe- are concerned about possible confound- sis. The final step in the research process is to ing variablesnot, which are variables related to communicate the study to a broader audience.

1.7 IMPORTANT TERMS Dostatistics (p. 1) research hypothesis (p. 3) theory (p. 5) scientific method (p. 3) variable (p. 3) independent variable (p. 5)

Chapter 1 | Introduction to Statistics 19

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. dependent variable (p. 5) confounding variable (p. 13) observational research population (p. 9) control group (p. 13) (p. 14) sample (p. 9) random assignment (p. 14) archival research (p. 14) measurement (p. 9) non-experimental research descriptive statistics (p. 16) level of measurement methods (p. 14) inferential statistics (p. 16) (nominal, ordinal, interval, quasi-experimental research ratio) (p. 9-10) (p. 14) experimental research survey research (p. 14) methods (p. 12)

1.8 EXERCISES 1. Listed below are a number of hypothetical a. “The use of color in a Yellow research hypotheses. For each hypothesis, Pages advertisement will increase identify the independent and dependent the perception of quality of the variable. products for a particulardistribute business a. Male drivers are more likely to when compared with noncolor exhibit “road rage” behaviors such as advertisements” (Lohse & Rosen, aggressive driving and yelling at other 2001, p. 75).or drivers than are female drivers. b. “We hypothesized that parents who b. The more time a student takes to finish use more frequent corporal and verbal a midterm examination, the higher his punishment . . . will report more or her score on the examination. problem behaviors in their children” c. Men are more likely to be members (Brenner & Fox, 1998, p. 252). of the Republican political party than post,c. “It was hypothesized that adolescents are women; women are more likely with anorexia nervosa would . . . be to belong to the Democratic political more respectful when compared with party than are men. peers with bulimia nervosa” (Pryor & d. Students who receive a newly Wiederman, 1998, p. 292). designed method of teaching reading d. “The purpose of the present will display higher scores on a test research was to assess brand name of comprehensioncopy, than the method recognition as a function of humor in currently used. advertisements. . . . It was predicted that e. The more time a child spends in participants would recognize product daycare outside of the home, the less brand names that had been presented he ornot she will be afraid of strangers. with humorous advertisements more 2. Listed below are a number of research often than brand names presented with questions and hypotheses from actual nonhumorous advertisements” (Berg & published articles. For each hypothesis, Lippman, 2001, p. 197). Doidentify the independent and dependent e. “The purpose of this study was to variable. explore the relation between time

20 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. spent in daycare and the quality of d. “We predicted that people in gain- exploratory behaviors in 9-month- framed conditions would show greater old infants . . . it was hypothesized intention to use sunscreen . . . than that . . . infants who spent greater those people in loss-framed conditions” amounts of time in center-based care (Detweiler et al., 1999, p. 190). would demonstrate more advanced e. “Students with learning disabilities exploratory behaviors than infants who received self-regulation training who did not spend as much time in would obtain higher reading center-based care” (Schuetze, Lewis, comprehension scores than students & DiMartino, 1999, p. 269). (with learning disabilities) in the f. “It was hypothesized that students control group” (Miranda, Villaescusa, would score higher on test items in & Vidal-Abarca, 1997, p. 504). which the narrative contains topics f. “We hypothesized that consumers and elements that resonate with would think that a ‘sale price’ their daily experiences versus test presentation distributewould generate a greater items comprised of material that is monetary savings than an ‘everyday unfamiliar” (Erdodi, 2012, p. 172). low price’ presentation” (Tom & Ruiz, 3. Listed below are additional research 1997,or p. 403). questions and hypotheses from actual g. “We hypothesize that physical published articles. For each hypothesis, coldness (vs. warmth) would activate identify the independent and dependent a need for psychological warmth, variable. which in turn increases consumers’ a. “It is expected that achievement liking of romance movies” (Hong & motivation will be a positive post,Sun, 2012, p. 295). predictor of academic success” 4. Name the scale of measurement (nominal, (Busato, Prins, Elshout, & Hamaker, ordinal, interval, ratio) for each of the 2000, p. 1060). following variables: b. “Men are expected to employ physical a. The amount of time needed to react to characteristics (particularly those a sound that are directly related to sex) more b. Gender often than copy,women in selecting dating c. Score on the Scholastic Aptitude Test candidates” (Hetsroni, 2000, p. 91). (SAT) c. “The purpose of our study was to d. Political orientation (not at all gain a better understanding of the conservative, conservative, very notrelationship between social functioning conservative) and problem drinking. . . . We e. Political affiliation (Democrat, predicted that problem drinkers Republican, Independent) would endorse more social deficits 5. Name the scale of measurement (nominal, Do than nonproblem drinkers” (Lewis & ordinal, interval, ratio) for each of the O’Neill, 2000, pp. 295–296). following variables:

Chapter 1 | Introduction to Statistics 21

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. a. One’s age (in years) “performance in college” at each of the b. Size of soft drink (small, medium, large, four levels of measurement? extra large) 7. A researcher hypothesizes that drivers who c. Voting behavior (in favor vs. against) use cellular phones will get into a greater d. IQ score number of traffic accidents than drivers who do not use these phones. For this e. Parent (mother vs. father) example, 6. A faculty member wishes to assess the a. What are the independent and relationship between students’ scores on dependent variables? the Scholastic Aptitude test (SAT) and their b. How could you measure the dependent performance in college. variable? a. What is a possible research hypothesis c. How could you conduct this study using in this situation? an experimental research method? How b. What are the independent and could you conduct this study using a dependent variables? non-experimental method?distribute c. How could you measure the variable or Answers to Learning Checks

Learning Exercise 1 2. a. IV: Instructors’ dress; DV: Expertise b. IV: Amount of television viewing; DV: Posttraumatic stress symptoms c. IV: Estimation of HSAS level; post,DV: Worry about terrorism d. IV: Use of humor; DV: Product recognition e. IV: Participation in intervention program; DV: Literacy skills

Learning Exercise 2 2. a. Nominal b. Ratio copy, c. Ordinal d. Ratio

Answers tonot Odd-Numbered Exercises

1. a. Independent variable (IV): Gender; Dependent Variable (DV): “Road rage” behaviors Dob. IV: Time; DV: Exam score c. IV: Gender; DV: Political affiliation

22 Fundamental Statistics for the Social and Behavioral Sciences

Copyright ©2016 by SAGE Publications, Inc. This work may not be reproduced or distributed in any form or by any means without express written permission of the publisher. d. IV: Method of teaching; DV: Comprehension test scores e. IV: Time in daycare; DV: Fear of strangers 3. a. IV: Achievement motivation; DV: Academic success b. IV: Gender; DV: Emphasis on physical characteristics c. IV: Alcohol drinking; DV: Social deficits d. IV: Framing; DV: Intention to use sunscreen e. IV: Training program; DV: Reading comprehension scores f. IV: Price presentation; DV: Perception of savings g. IV: Physical temperature; DV: Liking of romance movies 5. a. Ratio b. Ordinal c. Nominal distribute d. Interval e. Nominal or 7. a. IV: Cellular phone use; DV: Number of traffic accidents b. Example: Determine the number of traffic accidents each person has experienced in the past year. c. Example of experimental: Use a driving simulation with the “driver” talking on a phone and measure the number post,of potential driving mistakes or accidents. Example of non-experimental: Take a survey of the number of accidents people have been in and whether or not they were using a phone during the accident.

copy, Sharpen your skills with SAGE edge at edge.sagepub.com/tokunaga SAGE edge for students provides a personalized approach to help you accomplish your courseworknot goals in an easy-to-use learning environment. Log on to access: • eFlashcards • Learning Objectives • Web Quizzes • Media Links •Do Chapter Outlines

Chapter 1 | Introduction to Statistics 23